key: cord-261672-0cresfn8
authors: Kim, Sungchan; Jeong, Yong Dam; Byun, Jong Hyuk; Cho, Giphil; Park, Anna; Jung, Jae Hun; Roh, Yunil; Choi, Sooyoun; Muhammad, Ibrahim Malik; Jung, Il Hyo
title: Evaluation of COVID-19 epidemic outbreak caused by temporal contact-increase in South Korea
date: 2020-05-14
journal: Int J Infect Dis
DOI: 10.1016/j.ijid.2020.05.036
sha: 
doc_id: 261672
cord_uid: 0cresfn8

OBJECTIVES: On March 15, 2020, 61.3% of the confirmed cases of COVID-19 infection are associated with the worship service that was organized on February 9 in the Shincheonji Church of Jesus in Daegu, South Korea. In this study, we aim to evaluate the effects of mass infection in South Korea and assess the preventive control intervention. METHOD: Using opened data of daily cumulative confirmed cases and deaths, the basic and effective reproduction numbers was estimated using a modified susceptible–exposed–infected–recovered-type epidemic model. RESULTS: The basic reproduction number was estimated to be [Formula: see text]. The effective reproduction number increased approximately 20 times after the mass infections from the 31 st patient, which was confirmed on February 9 in the Shincheonji Church of Jesus, Daegu. However, the effective reproduction number decreased to less than unity after February 28 owing to the implementation of high-level preventive control interventions in South Korea, coupled with voluntary prevention actions by citizens. CONCLUSION: Preventive action and control intervention were fairly established in South Korea.

In December 2019, people in Wuhan, China began to contract pneumonia, and the cause was unknown.

The condition was similar to viral pneumonia, as confirmed by clinical presentation. On January 7, 2020, it was confirmed that the cause of the pneumonia was a new coronavirus. Thereafter, this was named the 2019 novel coronavirus disease-COVID-19. Notably, COVID-19 induces mild symptoms that are similar to those induced by other respiratory infections. However, particularly, it affects older people with comorbidity and can result in fatal respiratory diseases (Chen et al. 2020 ). On January 10, 2020, the Chinese authorities reported the first death due to COVID-19. After that, cases have been reported in other countries such as Thailand and Japan.

In South Korea, the first patient who had a history of visiting Wuhan, was reported on January 20, 2020.

Since then, confirmed cases of COVID-19 have been reported, and 30 patients were reported until in Daegu and that she attended the church service on February 9 and 16 after she had experienced the symptoms of COVID-19 on February 7. In addition, it was revealed that 5,006 confirmed cases, which accounted for 61.3% of the 8,162 confirmed cases, were associated with the church cluster in Daegu (Korean Ministry of Health and Welfare 2020). Accordingly, KCDC guessed that on February 9, the mass infections had occurred, resulting in many secondary cases, and so COVID-19 rapidly propagated in South Korea.

As COVID-19 rapidly spread nationwide from February 18, Koreans have actively worn masks since then.

Furthermore, the Government of Korea recognized the seriousness of the spread of COVID-19 and accordingly elevated the COVID-19 alert from level 3 to 4 (the highest level) on February 23. The government has implemented the social-distancing campaign, enhanced the infection prevention and control practices in hospitals, conducted drive-through testing, and postponed the schedule of school activities. It is still committed to preventing the occurrence of COVID-19.

In this study, we establish a mathematical model using the early data of confirmed cases that were reported from January 20 to March 15 in Korea. On the basis of the epidemiological investigation, the spreading process of COVID-19 during this period is divided into three phases. In addition, we estimate the reproduction number of each phase to analyze the transmission potential and severity of COVID-19.

Consequently, we assess the current situation of COVID-19 in Korea.

We use a modified susceptible-exposed-infected-recovered transmission model to evaluate the COVID-19 epidemic in Korea. Susceptible individuals enter the exposed class 1 after the transmission of the virus.

We consider the linear chains , = 1,2, ⋯ , on the exposed class for determining a model that can be fitted to the data with limited information that the mean incubation period is 1/ , fixed (Martcheva 2015; Champredon et al. 2018 ). The exposed people were infected and entered the class. The terms and denote isolated and discharged, respectively. The term ( ) denotes the transmission rate. The parameters 1/ and 1/ denote the average duration from onset of symptoms to isolated, and average duration from isolated to discharged, respectively. The parameter is the case fatality rate. We have the following:

To represent the temporal changes of contact, we consider the time-dependent transmission rate, ( ).

We assume the initial transmission rate to be constant, i.e., ( ) = 0 before = 1 . After = 1 , we assume that the transmission rate rapidly increases as ( ) = 1 . After = 2 , upon introducing a high level of preventive control campaigns, the transmission rate is assumed to exponentially decay at the rate (Althaus 2014) . We have the following:

Notably, the above-mentioned exponential decay implies that the change rate of , ′( ) is proportional to − ( ) with rate .

We introduce the following two key measurements that describe the infection spread: the basic reproduction number 0 and the effective reproduction number (Jones 2007) . The term 0 denotes the number of secondary infections generated by an infected case in wholly susceptible circumstances, and denotes the number of secondary infections generated in the current state of the population while implementing control interventions. A reproduction number higher than unity means continued disease transmission. However, the value lower than unity means that the continuous transmission has ended, and the disease gradually decreases and disappears. Particularly, the basic reproduction number 0 in our model is simply given as follows:

and the effective reproduction number, , is given as follows:

The total population size was assumed to be 50,000,000. We regard as a constant because the number of deaths is small, relative to the total population size. We used the method of least squares to estimate the model parameters to minimize the following sum of squared residual until the sampling time :

where Data ( ) and Data ( ) are cumulative data of the number of isolated and death at the th sampling time, respectively.

We used the daily cumulative cases and deaths data that were publicly available from the KCDC. We level to the highest so that the preventive action was strictly implemented. Therefore, we assume that 1 = 18 and 2 = 27(days).

We made some assumptions to reduce the number of our estimated parameters for fitting the data. First, the incubation period was fixed to 1/ = 5.1(days) as the average incubation-period estimate of the COVID-19 outbreak in Wuhan, China (Lauer et al. 2020) . It was reported 66 fatal cases as of March 12, 2020, and the time taken from experiencing symptoms to confirming is about 4.5 days and the time taken from test to confirming is about 0.5 days (Jeong et al. 2020 ). So, we used 1/ = 3(days) while assuming the presumed self-isolation to be approximately one day. The period from being isolated to discharged was taken to be 14.7 days from the data reported until March 13, 2020 from KCDC (Korean Ministry of Health and Welfare 2020). So, we used 1/ = 14.7 + 1.5 = 16.2(days) that was collaborated with our assumption. Transmission rate 0 , 1 , case fatality rate , and decay rate were estimated.

We considered 100-chain model. = 100 was obtained as a result of fitting with the condition 1/ = 5.1. 

In this study, we aimed to evaluate the effects of mass infection due to temporal increases in contacts and assess the preventive control interventions using the confirmed cases and deaths data associated with COVID-19 in Korea. The first patient was reported on January 20, 2020, but the transmission of the infection actually started from the 3rd confirmed patients from January 22 in Korea. Since then, the COVID-19 outbreak in Korea has resulted in 29 confirmed cases by February 18. In addition, it appeared that the outbreak was going to be controlled. It was shown that 0 = 1.77 in our model analysis. This is slightly lower than that of Wuhan, China ( 0 = 2.24~3.58) (Zhao et al. 2020) . Personal hygiene, such as wearing masks, handwashing and disinfecting items, seemed to have been maintained a certain level, Thus far, the COVID-19 outbreak is ongoing in many countries. For example, as of March 23, 2020, countries such as Italy, the United States, Spain, Germany, and France still have more than 3,000 confirmed cases per day and more than 100 deaths per day. However, in Korea, the outbreak has been reduced, as confirmed by the value of to less than unity within 10 days after the first mass infection was noticed. Accordingly, we suggest that the government policy of "social distancing" which had been implemented in Korea until April 5 and extended to May 5 may be maintained even at a lower level. 

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